find the volume of a regular polygon inscribed in a triangular prism in php

To find the volume of a regular polygon inscribed in a triangular prism, we'll need to follow these steps:

  1. Determine the apothem of the regular polygon inscribed in the triangular base of the prism.
  2. Calculate the area of the regular polygon.
  3. Compute the volume of the inscribed polygon by multiplying its area by the height of the prism.

Here's the code in PHP:

main.php
<?php

// Define the number of sides of the inscribed regular polygon.
$numSides = 6;

// Define the height of the triangular prism.
$height = 10;

// Define the length of the base of the triangular prism.
$base = 8;

// Define the radius of the circumscribed circle of the inscribed regular polygon.
$radius = $base / (2 * sin(pi()/$numSides));

// Calculate the apothem of the regular polygon.
$apothem = $radius * cos(pi()/$numSides);

// Calculate the area of the regular polygon.
$area = 0.5 * $numSides * $radius * $apothem;

// Calculate the volume of the inscribed polygon.
$volume = $area * $height;

// Print the result.
echo "The volume of the inscribed regular polygon is: " . $volume;

?>
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In this example, we assume that the triangular prism has a regular triangular base with length 8 and height 10. The inscribed regular polygon has 6 sides. The code calculates the volume of the inscribed polygon and outputs it on the screen.

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